A comparison is made of the different ways in which an ionized gas may change the velocities of fastmoving protons. It is found that a beam with a very well-defined velocity may lose its kinetic energy through the excitation of unstable oscillations, but it seems most unlikely that the stringent conditions necessary for this process will ever occur in any astrophysical application. Single protons lose energy by leaving a wake in the plasma (Pines and Bohm 1952). If sufficiently intense plasma oscillations are excited, the protons may also gain energy through acceleration in random electric fields. Fast electrons can accelerated even more efficiently in this way.
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F. D. Kahn (1959) studied this question.